WASHINGTON (CNN) -- It happens immediately after any high-level White House official resigns his or her post -- political observers and Washington reporters go into overdrive over possible replacements.

Name dropping about who will replace Alberto Gonzales started moments after he stepped down.

The scenario played out Monday, when moments after news surfaced that Alberto Gonzales was stepping down from his post as attorney general, senior administration officials told CNN that current Homeland Security Secretary Michael Chertoff would likely get the nod.

If true, it would be "a surprise to Mike," another source later told CNN.

Yet other senior administration officials started knocking down such reports, telling CNN that Chertoff's role in Hurricane Katrina's aftermath could raise problems during Senate hearings.

Did things really change that quickly? Which sources had better information? What are the rules of engagement in the name-dropping game?

Ari Fleischer, who served as President Bush's first press secretary, says the back and forth on Chertoff speculation is "a parlor game that is Washington at navel-gazing best. Washington loves to guess -- even if they guess wrong."

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"Individuals want a reporter to float his or her name because it's probably good for reputation or business, and reporters can't resist," Fleischer said. "There's no downside to it because nobody goes back to these reporters and asks, 'Why did you say it was this person and on what basis did you say it?'"

Paul Begala, a former adviser to President Bill Clinton, says White House officials often float a "trial balloon ... so it can be shot down."

"President Bush is both petulant and predictable," Begala said in a CNN interview. "Knowing this, people who oppose someone [like Chertoff] will float the name," and in turn, "annoy Bush and kill the potential nominee."

The administration is "playing you guys," a congressional source with close ties to the Department of Justice told CNN.

Bush administration officials say no decision has been made on who will succeed Gonzales. White House spokesman Scott Stanzel said the president was committed to picking a "high-caliber" nominee for the nation's top law-enforcement post, but declined to discuss possible candidates.

Whether it's individuals, reporters or administration officials hyping potential replacements, the speculation often turns out to be inaccurate.

"I remember when Scott McClellan left the job as press secretary, and before Tony Snow got named, I already knew Tony was going to get named," Fleischer said. "But I read so many names of people under consideration when I knew the White House hadn't even talked to those people."

But that didn't stop more possible Gonzales successors from surfacing throughout the day -- and later being shot down.

Officials close to the White House and the Justice Department started floating several other names purportedly under consideration, including Larry Thompson, the former deputy Attorney General until 2003, and now general counsel for PepsiCo.

But, despite all the talk, a senior administration official later said Thompson is no longer being considered.

Other potential prospects include former Solicitor General Ted Olson, a GOP stalwart who argued Bush's case before the Supreme Court in the 2000 Florida recount, and George Terwilliger, a former Bush campaign lawyer who also served as the Justice Department's No. 2 man under the president's father.

Meanwhile, another congressional aide told CNN that U.S. Circuit Judge Laurence H. Silberman, current Solicitor General Paul Clement and former Sens. Slade Gorton, John Danforth and Asa Hutchinson are also under consideration for the post.